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The iterated Carmichael lambda function Harland, Nicholas

Abstract

The arithmetic function λ(n) is the exponent of the cyclic group (Z/nZ)^x. The k-th iterate of λ(n) is denoted by λk(n) In this work we will show the normal order for log(n/λk(n)) is (loglog n)k⁻¹}(logloglog n)/(k-1)! . Second, we establish a similar normal order for other iterate involving a combination of λ(n) and Φ(n). Lastly, define L(n) to be the smallest k such that λ_k(n)=1. We determine new upper and lower bounds for L(n) and conjecture a normal order.

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Attribution 3.0 Unported

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